7. Optimum Trajectories for a Reaction-Propelled Vehicle in a Central Field. V. I. Gurman, p. 277.

8. Calculation of Partial Derivatives of Motion Characteristics from Initial Conditions. V. G. Khoroshavtsev, p. 282.

9. Predicting the Motion of Spacecraft about the Mass Center. V. N. Borovenko, p. 288.

10. Radiation Control of the Orientation of Space Probes. E. B. Galitskaya and M. I. Kiselev, p. 298.

11. An Analysis of Trajectories for Interplanetary Flight with Constant-Power Motors. V. V. Beletskii, V. A. Egorov, and G. G. Ershov, p. 397.

12. Investigation of the Motion of a Spacecraft in the Atmosphere. N. I. Zolotukhina and D. E. Okhotsimskii, p. 414.

13. Generalized Newton's Method for Solving Boundary-Value Problems. V. A. Vinokurov and Yu. N. Ivanov, p. 423.

14. A Rotation of the Orbital Plane of a Satellite. Yu. M. Kopnin, p. 428. 15. Asymptotic Stable Time-Stationary Rotations of a Satellite. V. A. Sarychev, p. 537.

16. The Stability of Steady Rotation of a Satellite in an Elliptical Orbit. A. P. Markeev, p. 544.

17. Study of Plane Flexural Vibrations of a Gravitationally Stabilized System. V. I. Popov and V. Yu. Rutkovskii, p. 547.

18. A Remarkable Property of a Pencil of Hyperbolic Trajectories. A. A. Dashkov and V. V. Ivashkin, p. 553.

19. Optimum Rotation of the Plane of a Circular Orbit by the Application of a Transverse Force. Yu. N. Ivanov and Yu. V. Shalaev, p. 556.

20. A Series Solution to the Three-Body Problem. A. N. Bogaevskii, p. 563. 21. On the perturbing Moment of a Satellite Moving in the Earth's Magnetic Field. A. D. Shevnin, p. 568.

APPENDIX III. THE STORY OF EARTH'S ATMOSPHERE

Robert F. Fellows, Program Chief, Planetary Atmospheres, Office of Space Science and Applications, National Aeronautics and Space Administration

INTRODUCTION

An atmosphere is the gaseous envelope surrounding a celestial body. It stands between the body, a planet for example, and all external influences. Over the past two decades research on planetary atmospheres has involved so many lines of attack that one may have gained the impression that the work was made of bits and pieces. In one sense this is so, but the results now permit us to relate these bits and pieces into a more total or comprehensive picture of the Earth's atmosphere. The picture is by no means complete, but sufficient detail has been acquired and placed in position that the pieces are showing their overall relation, very similar in fact to the assembly of a jig-saw puzzle.

HIGHLIGHTS OF PROGRESS

The following description of some selected "highlights" of research in the Earth's atmosphere may serve to illustrate the above point.

The International Geophysical Year (IGY) provided the basis for the scientific exploration of the Earth's atmosphere with sounding rockets and satellites. One of the most important IGY results was the summary picture of our atmosphere that emerged. The upper atmosphere was found to be more complex and to undergo greater variations in temperature and density than had been expected.

In 1959, within the first year after its formation, NASA initiated a sounding rocket program to follow through on the IGY results and to investigate the many unexpected questions that had become apparent. A sounding rocket project to study upper atmospheric winds was initiated and about this same time the first upper atmospheric seasonal temperature variations from Fort Churchill, Canada, were obtained. These reports were especially intriguing because lower temperatures were found in the summertime than for the winter months in the region of the atmosphere around 50 miles in altitude.

By late 1960 sufficient density data were available from drag measurements of early satellites that a diurnal bulge was recognized. This bulge is a swelling or

around the Earth and reaches a maximum at about 2:00 p.m. local time. It is a result of the heating effect of solar energy acting on the atmosphere. Also, about this same time the presence of hydrogen in significant amounts in the upper regions of the atmosphere was detected. This property is often referred to as the hydrogen geocorona. The finding was of considerable importance because it bears ultimately on the quantitative aspects of the loss of water from the Earth. This is because water that diffuses sufficiently high into the atmosphere (above approximately 75 miles) is dissociated by the energetic solar ultraviolet radiation into oxygen and hydrogen.

By 1961 sufficient data were available from many separate experiments to permit Nicolet to predict that helium must be a significant component of the atmosphere somewhat below the level in which hydrogen predominated. It was also in this year that the first preliminary results on the measurement of solar extreme ultraviolet radiation and its absorption in the upper atmosphere became available. The first twelve-foot sphere (balloon satellite, Explorer IX) for determination of atmospheric density was launched about this time. This satellite demonstrated the potential for extended density studies by this relatively inexpensive approach.

In 1962 the first measurements which questioned the commonly assumed premise of thermal equilibrium of ions and electrons in the ionosphere were obtained. These data stimulated further research in the next few years that indicated greater complexity of phenomena than could be explained by existing models and theories. The postulate by Nicolet of the previous year was verified when experimental data from the Explorer VIII satellite showed the presence of helium ions in the expected altitude region. The sounding rocket program was well underway by this time, and the first spectrometer measurements of the ultraviolet airglow and the first direct measurements of changes in the ionosphere during a solar eclipse were obtained.

In 1963 the first satellite designed specifically for studies of the aeronomy of the upper atmosphere was launched. This satellite, Explorer XVII provided the first in situ simultaneous measurements of atmospheric composition, density, and electron content on an extended scale. The results were the first integrated picture of the Earth's atmosphere and its variations in the altitude region studied. This same year produced the first measurement of nitric oxide in the atmosphere. This was accomplished by an ultraviolet spectrometer experiment carried by a sounding rocket. A concentration about tenfold greater than predicted by theory was found. This result has led to a re-examination of pertinent theories and models, and to a reappraisal of the laboratory measurements of reaction rates used to calculate the predicted amount.

In 1964 the first Orbiting Geophysical Observatory was launched. One of the summary findings from this mission was the first evidence linking variations in ion composition of the upper atmosphere with changes in the Earth's magnetic field. Also, by now sufficient data had been accumulated from sounding rocket measurements to indicate that strong winds and wind shears were a regular property of the 50 to greater than 150 mile altitude region of the atmosphere on a global basis.

In 1965 we launched OGO-II, the first observatory payload instrumented primarily for aeronomy and ionosphere studies. Results from this mission extended our knowledge of the relations between ion composition, magnetic field variations and solar behavior. The question of non-equilibrium of ion and electron temperatures raised in 1962 was being investigated thoroughly by this time and precise results were now becoming available to permit a quantitative assessment of this problem. This work was of great importance because the question of equilibrium, or an assumption of equilibrium in a model is a determining and critical step in the development of a realistic theory describing atmospheric processes.

In 1966 the second aeronomy satellite, Explorer XXXII was launched to continue the investigations initiated by Explorer XVII and to extend our knowledge of atmospheric behavior on a global basis. In this same year reports of preliminary measurements by mass spectrometers carried by sounding rockets into the "D" region of the ionosphere indicated the presence of heavy ions with mass greater than 48 atomic mass units. These measurements are difficult to make and require specially developed instruments. The heavy ions have aroused considerable interest and their identification awaits further research. Two prin

atmospheric components such as nitrogen oxides, carbon oxides, and possibly water, or the ions may be elements, the components of meteoritic dust. Present evidence and theory indicate the latter to be a strong possibility.

A PRACTICAL APPLICATION

The reader may well ask himself the question, "This all sounds fine and very impressive, but what does it mean to me and to those who are not specialists in this field?" It is not easy to answer that question concisely. The pathways for the transfer of the results of basic science into new technology for mankind's benefit are usually broad and diffuse. An advance in one scientific discipline sometimes accelerates progress in fields far removed from the focal point of the original work. Often it is only years later that the real significance and impact of a new scientific finding become realized. Even in retrospect it is difficult to trace the communication train and sequence of steps involved in cross-discipline transfers of knowledge.

An example which is subject to concise description is the use of the results and latest findings to produce a description of the atmosphere in the form of a widely accepted "standard" or "model" description of the atmosphere. A "Standard Atmosphere" is a carefully evaluated summary compilation of the latest and best information available describing the conditions and character of the atmosphere for specified parameters, for instance from sea level to very high altitudes. Thus, it provides a common frame of reference for many scientific and technological undertakings. For example, in preparing designs of advanced aircraft and in evaluating performance specifications it is essential that all work be based on the same description of the atmosphere. Otherwise, no comparison of alternative designs could be meaningful. Obviously, the actual performance of an airplane which is designed on the basis of an unrealistic model atmosphere may be very different from the desired or specified performance. In addition to fulfilling the above needs, model atmospheres also serve as a necessary "yardstick" against which scientists and engineers can evaluate experimental results. For instance, measurements by many experimenters of the specific characteristics of the atmosphere under changing conditions are often compared to the properties specified in a model atmosphere. This comparison against a common reference permits an identification of areas of agreement and critical areas for further effort. A model or standard atmosphere table is essential for the design of airplanes, balloons, and the Mercury, Gemini, Apollo, and unmanned reentry spacecraft.

The need for a standard model of the atmosphere was recognized early in the history of aviation. In 1922, the first U.S. Standard Atmosphere Model was prepared by the National Advisory Committee for Aeronautics, the predecessor organization to NASA. As more and better information became available the model was periodically revised and extended to higher altitudes complimentary to the increasing capabilities of more recently developed aircraft. In 1952 the data were extended to include the results then becoming available from early sounding rocket investigations into the upper atmosphere. Later, with the coming of the satellite age, it was possible to extend the data still higher in altitude and to make the model much more comprehensive. The current U.S. Standard Atmosphere was printed in 1962. The next version to be titled "U.S. Standard Atmosphere Supplement, 1966," will be available in early 1967.

THE PRESENT ATMOSPHERE

We will now explore some fundamental questions concerning the origin, evolution, and changing nature of the Earth's atmosphere, and the close relation and mutual dependence of an atmosphere and its planet.

The largest energy source operating on the atmospheres of the planets (at least for the terrestrial ones) is solar illumination. Radiation from the Sun falls on the illuminated portion of the Earth's atmosphere at a rate of two calories per square centimeter per minute (1,400 watts per square meter). This is called the solar constant. The bulk of this energy lies in the narrow visible region of the spectrum. Much of this energy along with some infrared penetrates to the surface where it is absorbed by the ground, although a substantial fraction is rejected by being reflected from clouds. The wavelengths outside the visible region (x-ray, ultraviolet and infrared) are absorbed at various levels in the atmosphere and although the energy involved is only a small part of the solar

The energy that is absorbed heats the atmosphere and also produces chemical changes by breaking molecules into atoms and by ionizing components of the atmosphere. Temperature and density differences occur, and mass air motions result.

Other effects of this absorption of solar radiation by the atmosphere are not immediately obvious. The atmosphere protects life on the Earth from the injurious effects of the far ultraviolet solar radiation, and from particles occurring elsewhere in space. These particles include solar and galactic cosmic rays which are high-energy electrons, hydrogen atoms, and other atoms; and the much, much larger particles called meteorites.

The visible radiation from the Sun, except for the fraction reflected by clouds or scattered in the atmosphere, penetrates to the surface and is absorbed by the ground. Thus, the Earth's surface is heated by an appreciable fraction of the solar energy. The Earth in turn emits radiation at an intensity and in a wavelength interval determined by its temperature. For the average temperature of the surface this wavelength interval has its maximum in the far infrared region of the spectrum. Several constituents of the atmosphere, notably water, carbon dioxide, and ozone, are strong absorbers of this far infrared radiation. The absorption of this energy heats the lower atmosphere which in turn reradiates energy—part upward into space and part downward to provide additional heating to the surface. This return of infrared energy from the atmosphere is referred to as the "greenhouse" effect. The combination of direct solar heating and the greenhouse effect heat the Earth's surface to an average temperature of about 60 degrees Fahrenheit.

Clouds are composed of water vapor and therefore are strong absorbers of the surface emitted infrared energy. Consequently, they produce a strong and variable greenhouse effect. All of us are familiar with the greater rate with which temperature drops on a clear cloudless night as compared to a night when the sky is covered with thick clouds. This is an effect of clouds which is in addition to their effect as reflectors of part of the incident solar energy. Thus, the Earth's cloud cover is a very important factor in determining energy inflow and outflow and thereby surface temperature.

Although the atmosphere on Earth seems thin to us, the weight of the atmosphere averages out to about two million tons per inhabitant. On the other hand, if the atmosphere were condensed into a uniform layer having the density of water, the layer would be only about 30 feet deep all over the entire globe. Atmospheres are described and studied in terms of composition, temperature, and pressure, and the variations of these quantities with altitude. This is insufficient, however, because the complex mass motions resulting from heating, and the chemical changes that result in the ionization of certain species, produce phenomena in the atmosphere that are more complicated to describe. We now know that the atmosphere of the Earth is very dynamic, it is continually changing in properties with time of day, season, year, and solar cycle. We determine the description of the atmosphere at the time of a measurement, and it is variations from the average that are significant in understanding the short-time processes of the atmosphere. The long-time variations refer to the fundamental questions to be discussed near the conclusion of this paper.

Figure 184 summarizes a great deal of information pertaining to the Earth's atmosphere. The curve on the right hand side plots temperature against altitude. Notice that as the altitude increases from sea level, the atmosphere tends to become cooler to about 8 miles altitude, then it warms to a maximum at an interval of around 18 miles, then it cools again to another minimum around 60 miles. Above this altitude the temperature increases very, very rapidly reaching values as high as 2000 degrees Fahrenheit above 150 miles. At still higher altitudes the temperature is isothermal with altitude. The temperature is cool enough at the minimum shown around 60 miles that most of our water is kept below this altitude in the atmosphere; it is frozen out when it reaches this region and cannot diffuse rapidly into the higher atmosphere where solar ultraviolet light would decompose it into oxygen and hydrogen.

Above 110 kilometers the atmosphere becomes so thin that the light atoms and molecules tend to rise in the atmosphere and ride above the heavier molecules under the action of the Earth's gravity field. This process is called diffusive separation.

As I mentioned previously, solar ultraviolet radiation ionizes atoms and

above approximately 35 miles and imparts unique and special characteristics to this region. The effect of these electrons on the propagation of radio waves is so important that the detailed study of the ionospheric aspects of the atmosphere is a discipline in its own right in the NASA program.

Some of the properties of the ionosphere are shown in figure 185. Depending upon the conditions of the ionosphere, that is the number of electrons present per cubic centimeter and upon the frequency of the radio waves, absorption, reflection, or refraction of the radio waves can take place. Obviously, if refraction takes place when we are tracking spacecraft, corrections must be made to obtain the actual position from the apparent position of the spacecraft. A very common analogy of this is the fact that when we look at a long stick which is partially immersed into water, the stick appears bent at the surface due to the refraction of light rays going from a medium of one density to another.

EVOLUTION OF OUR ATMOSPHERE

One of the basic objectives of the planetary atmospheres program is to understand the relationship of an atmosphere to its planet and to arrive at an understanding of the origin and evolution of the atmosphere. An understanding of the history of the Earth's atmosphere will contribute to a clearer picture of other planetary atmospheres which necessarily must be studied with much more fragmentary data; and, conversely, information about other atmospheres is helpful in better understanding the Earth's. While most of us appreciate the fact that the atmosphere is necessary for the existence of life, it is not so often that we realize that, if it weren't for life, we would not have an atmosphere of the type we have today.

A discussion concerning the probable evolution of the Earth's atmosphere brings forth the cross-discipline relationships that exist between the planetary atmospheres discipline and other disciplines. Our present thinking represents the following sequence. Geologic evidence indicates that our present atmosphere differs from the primitive atmosphere that may have accumulated during the